JP2010518390A - Method and apparatus for determining the state of charge (SoC) of a rechargeable battery - Google Patents

Abstract

  The present invention relates to a method for determining a state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery. The invention also relates to a method for measuring the relationship between state of charge (SoC) and EMF. The invention further relates to a device for determining the state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery.

Description

  The present invention relates to a method for determining the state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery. The invention also relates to a method for measuring the relationship between state of charge (SoC) and EMF. The invention further relates to a device for determining the state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery.

  Showing an accurate and reliable state of charge (SoC) is an important feature in any device powered by a rechargeable battery. Accurate and reliable SoC instructions allow users to use the entire available battery capacity and prevent unnecessary charging that will expedite battery drain. Many methods for SoC indication have been published and patented. Basically, these methods are separated into two groups. That is, the direct measurement method and bookkeeping as described in the book by HJ Bergveld et al., “Battery Measurement System-Design and Modeling”, Philips Book Series, vol. 1, Kluwer Academic Publishers, 2002, Chapter 6. It is a method.

  In the case of direct measurement, battery variables such as terminal voltage, impedance, current or temperature are measured, and this measured value is directly converted to a SoC value based on, for example, a look-up table or function. The main advantage of this group of methods is that when the SoC indication system is connected to the battery, the measurement starts immediately and the SoC is determined. The main problem with this group of methods is that it is extremely difficult to include all relevant battery behavior in a lookup table or function. This means that it is difficult for the user to predict the situation of the reference table or function, and the SoC needs to be obtained by interpolation or extrapolation of tabular data. This leads to a decrease in the predicted SoC accuracy.

  In the past, Philips Research has patented that so-called electromotive force (EMF) is a useful battery variable for direct measurement SoC indications, as described in US Pat. No. 6,420,851. EMF is the difference between the positive and negative equilibrium potentials. When the battery is in equilibrium, that is, no external current is flowing and the battery voltage is sufficiently relaxed from the previous charging / discharging current application. Can be measured at the battery terminal. By measuring the battery voltage under equilibrium conditions, the measured voltage value is converted to a SoC value via the EMF = f (SoC) relationship stored in the system. This storage curve can be obtained in the laboratory by the SoC instruction system manufacturer in several ways, including interpolation, extrapolation, and relaxation. The advantage of the EMF = f (SoC) relationship is that it provides an indication of the SoC during equilibration based on battery voltage and temperature measurements. However, this method does not work until the battery voltage is sufficiently relaxed during or after energization of the external current. This is because the battery terminal voltage is not equal to EMF in this case.

  The method of the bookkeeping method group is based on coulomb calculation, ie measuring the current flowing into and out of the battery as accurately as possible and integrating the net current. This method provides a good SoC indication when the battery is of linear capacity. Unfortunately, this is not common. For example, the stored charge is not available to the user under all conditions, for example, due to diffusion limitations or when the battery is unused, the charge on the battery slowly decreases due to self-discharge. . Most of this battery-related behavior is highly dependent on temperature and SoC, so the coulomb calculation needs to be adjusted, for example, by reducing the calculation count occupied by self-discharge, depending on the battery SoC indication system and temperature. is there. The main advantage is that the amount of tabular data can generally be reduced compared to direct measurement systems. The main problems are: (i) the system needs to be connected to the battery at all times, (ii) the system cannot grasp the SoC at the first connection (program the integration start point) (Iii) A calibration point is necessary.

Based on the aforementioned findings, Philips Research has developed a method for directing SoC. This method combines the advantages of direct measurement and bookkeeping with an adaptive and predictable system and is shown in US Pat. No. 6,515,453. The main feature of this method is that SoC prediction is done by voltage measurement when the battery is in a so-called equilibrium state and by current measurement when the battery is in an unbalanced state. In equilibrium, no or little external current flows and the battery voltage is completely relaxed from the previous charge or discharge. As described above, the measured battery voltage is substantially equal to the EMF of the battery in equilibrium. Therefore, the EMF method can be applied under these conditions. When the battery is in an unbalanced state, the battery is in a charge or discharge state, and the charge released from or supplied to the battery is calculated by current integration. This charge is subtracted from or added to the previously calculated SoC value. In addition to predicting the SoC, which is an indicator of the amount of charge still remaining in the battery, the method can also predict the remaining operating time for application under predetermined conditions. This is done by predicting the time required for the battery voltage to drop below the so-called discharge completion voltage _VEoD . This is the minimum voltage at which the application no longer works. To predict this time, based on the current value of the SoC, the stored EMF curve and the so-called overvoltage function, the battery overvoltage at the completion of discharge is predicted for the selected load condition. When the battery is discharged, its voltage can be obtained by subtracting the overvoltage from the EMF value. Overvoltage depends on several factors including SoC, current, temperature and time, and also on factors such as the series resistance of the electrodes. This patented method can later introduce several methods for addressing battery aging, calibrating and updating parameter values, as described in WO 2005/085889. To be expanded. Recently, new measurement methods have been obtained and published within the scope of the ph.D. project. Improvements have been made mainly for better use of the battery function, ie the function of the EMF curve and overvoltage: V. Pop, HJ Bergveld, PHL Notten, PPL Regtien, “State of charge indication in mobile applications”, Industrial Electronics (ISIE2005) IEEE International Symposium, vol.3, pp.1007-1012, Dubrovnik, Croatia, June 20-23, 2005; V. Pop, HJ Bergveld. PHL Notten, PPL Regtien, “Small and Accurate in Mobile Applications Do charge status indication ", 6 ^th IEEE International conference, Power Electronics and Drive Systems (PEDS2005 ), vol.1, pp.262-267, Kuala Lumpur, Malaysia, Nov.28-Dec. 1, 2005 and V. Pop, HJ Bergveld. PHL Notten, PPL Regtien, “Real-time evaluation system for charging state indication algorithm”, Proceedings of the Joint International IMEKO TC1-TC7 Measurement Science Symposium, vo.1, pp.104-107, Illmenau, Germany, Sept.21 -24, 2005.

  The advantage of the SoC indication method described above is that, after the current step is applied, during the charge / discharge cycle, the SoC obtained by Coulomb calculation is calibrated based on voltage measurement, EMF application, and voltage prediction method. is there. This is significant compared to commercially available bookkeeping systems. In commercial bookkeeping systems, typically one or more calibration points, ie, “battery full” (defining charge) and “battery empty” (which, under certain conditions, are less than the discharge completion voltage, are not often encountered. Is only used). In other words, the proposed system is calibrated more frequently than the existing bookkeeping system, which increases the accuracy while maintaining the benefits of the bookkeeping system.

Another feature of the aforementioned SoC indication system is that the available remaining operating time under discharge conditions can be predicted as a function of overvoltage. To calculate the remaining operating time, the SoC ₁ value is calculated at the beginning of the discharge state by the overvoltage calculation and the EMF model.

  It is important that the SoC indication system can accurately determine the EMF and overvoltage of the battery. The first solution is to store the SoC = f (EMF) value in the form of a reference table, which is V. Pop, HJ Bergveld, PHL Notten, PPL Regtien, state-of-the-art state-of-charge determination, Measurement Science and Tecnology Journal, vol.16, pp.R93-R110, December, 2005. The reference table is a table in which constant values of measurement parameters are stored and used for instructions from the SoC. The size and accuracy of the lookup table in the SoC instruction system depends on the number of stored values.

  The main problem with this method is that it is difficult to provide an accurate SoC indication system that takes into account each point of the EMF curve, even for a single battery type. When many measurement points are included, this method becomes more complex, more expensive than other methods, and cannot provide any significance.

  Alternatively, a physical EMF = f (SoC) model for a Li-ion battery is shown in the book by Bergveld et al. The idea of this model is that the corresponding SoC can be calculated at a certain EMF and temperature. The EMF curve is measured by linear interpolation, linear extrapolation, or voltage relaxation methods, approximated by a mathematical EMF = f (SoC) function, and the EMF of a lithium ion battery with intercalating electrodes is positive and negative Modeled as the difference in equilibrium potential between the two. By using this function for each SoC value, the EMF is calculated. The EMF = f (SoC) model shown by Bergveld et al. Is fitted to the measured EMF curve. FIG. 1 shows the modeled EMF curve used in the system, but good fitting is obtained between the measured measurement curve and the reference battery tester at all temperatures. This figure shows the SoC prediction error when using a measurement curve and when using a modeled EMF curve.

  Figure 1 shows that the maximum error in an SoC is 1.2% for an SoC of approximately 16% at 5 ° C. However, in the above-described method, it is necessary to perform mathematical inversion in order to obtain the SoC value based on the EMF measurement from the EMF = f (SoC) relationship. This means that mathematical calculations can reduce the accuracy of SoC calculations. The method presented here proposes a new SoC = f (EMF) model, in which case the need for mathematical inversion is eliminated.

Battery overvoltage is defined as the difference between battery EMF and battery charge / discharge voltage. Due to overvoltage, the battery voltage is (lower) higher than the battery EMF voltage during the (discharged) charge state. The value of the battery overvoltage depends on the charge / discharge C rate current, the charge / discharge time, the SoC, the temperature, the battery response, and the duration of use (aging). In addition, the remaining operation time can be predicted by overvoltage prediction. When current flows from the discharging battery, overvoltage occurs. Even though a certain amount of capacity still remains in the battery, the battery appears empty to the user. This is because the battery voltage falls _below a discharge completion voltage (V _EoD ) (for example, 3 V in the case of a lithium ion battery) determined in the portable device. This is illustrated in FIG. In the figure, the residual operating time _tr is plotted against the horizontal axis to illustrate this effect.

As shown in FIG. 2, discharging starts at point A, and the battery voltage decreases with overvoltage η. The overvoltage is a function of the discharge current I and the temperature T. At this point, residual operating time t _r = t _i is calculated based on the following formula:

ここで、Q_A[C]は、放電開始時点Aでのバッテリ容量であり、Q_B[C]は、点Bでのバッテリ容量を表し、以下の式で計算される：

Here, Q _A [C] is the battery capacity at the discharge start time point A, and Q _B [C] is the battery capacity at the point B, and is calculated by the following formula:

ここで、SoC（EMF_B）[％]は、点Bでの予測EMFに基づいて計算された、SoC₁値を表し、Q_maxは、バッテリの最大容量を表す。予測EMF_Bは、放電完了電圧と予想過電圧ηとの合計である。

Here, SoC (EMF _B ) [%] represents the SoC ₁ value calculated based on the predicted EMF at point B, and Q _max represents the maximum capacity of the battery. The predicted EMF _B is the sum of the discharge completion voltage and the predicted overvoltage η.

At point B, t _r = t _s and under the current conditions of I and T, the remaining available capacity is zero. When the battery voltage reaches the discharge completion voltage, the battery is completely emptied (point t _r = t _{empty in} FIG. 2), and the overvoltage is zero. Thus, the remaining operating time is represented by the contrast between the available charge in the battery (ie SoC) and the charge that can be drawn from the battery under certain conditions.

The SoC algorithm shown above was implemented for the extended condition range, ie, the evaluation set at different starting SoC values (SoC _st ), C rate current, and temperature, to verify the accuracy of the SoC and remaining operating time. For evaluation, a new US18500G3 Li-ion battery manufactured by Sony was used. During the first charge cycle using the method described in WO-2005085889, the maximum battery capacity was 1177 mAh. Table 1 summarizes the experimental results. The discharge C rate current and temperature T (° C.) used in these tests are shown in the first and second columns, respectively. The experimental SoC [%], SoC _st , and SoC ₁ shown at the start are shown in the third and fourth columns, respectively. The fifth, sixth, seventh and eighth columns show the predicted t _rstp residual operating time at the start of the experiment, and the measured t _rstm residual operating time, the error t _re [min] of the residual operating time at the end of the experiment, and It represents the relative error of the remaining operation time _trre [min]. The estimated remaining operating time (min) at the start of the experiment is expressed as SoC _st [%], SoC ₁ [%], maximum capacity Q _max [mAh], and discharge current I _d [A] (Equation 1 and (See also 2):

残留運転時間誤差は、3Vの放電完了電圧レベルで、リアルタイムのSoC評価によって計算された、残留運転時間値に等しい。残留運転時間の相対誤差は、

The residual operating time error is equal to the residual operating time value calculated by real-time SoC evaluation at a discharge completion voltage level of 3V. The relative error of the remaining operating time is

で表される。

It is represented by

[Table 1] Results obtained using the SoC algorithm with reference to the extended range of conditions described above

From Table 1, it is not sufficient to accurately model the relationship between EMF = f (SoC) (see Fig. 1) and overvoltage in order to obtain high accuracy for the remaining operating time. For example, starting discharge from a 40.2% SoC shows a residual operating time of 47.5 minutes at 0.5 ° C rate current and 25 ° C. However, after 37.3 minutes, the battery reached a level of 3V. This means that the SoC system shows 10.2 minutes of inaccuracy in the remaining operating time. In this example, the error in the remaining operation time _trre is calculated as 27.3% (see Equation 4).

U.S. Pat.No. 6,515,453

  In the present invention, a new method is proposed for indicating the SoC and remaining operating time with high accuracy, replacing the EMF = f (SoC) and overvoltage model.

In particular, the present invention is a method for determining the state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery,
Defining a function including a parameter between the state of charge (SoC) and the electromotive force (EMF) of the rechargeable battery;
Measuring a plurality of values of the state of charge (SoC) of the rechargeable battery as a function of the electromotive force (EMF);
Fitting the parameter of the function to the result of the measurement;
Storing the function including fitting parameters in a memory;
Obtaining the electromotive force; and
Putting the measured value of the electromotive force into the function;
Reading the state of charge (SoC);
Is provided.

In the present invention, the state of charge (SoC) of the rechargeable battery is a device that determines the function of the electromotive force (EMF) of the battery,
Means for determining the state of charge and the EMF in the battery;
A memory adapted to store a parameterized relationship between the state of charge (SoC) and the electromotive force (EMF) of the rechargeable battery;
Means for adapting the parameters of said relationship;
Is provided.

  This method and instrument provides a new method for modeling that avoids the inaccuracies inherent in inverse functions. In addition, the model can be adapted to the measurement results by adapting the parameters. The advantage is that it does not use mathematical inversion as in the conventional method. This advantage facilitates method adaptation and can be easily used for portable applications compared to the conventional EMF = f (SoC) method.

In the conventional SoC instruction method, an accurate SoC calculation is obtained by the EMF model at equilibrium, and the remaining operation time can be accurately calculated during discharge under any load condition. When using the method of determining the SoC by EMF and predicting the remaining operation time, it seems most preferable to use SoC = f (EMF) and SoC ₁ model. However, methods known in the literature use mathematical inversion for EMF calculations, or use SoC ₁ calculations with overvoltage prediction, full voltage measurements under load conditions and EMF model calculations during the full SoC range. To do. This is problematic in that the accuracy of the remaining operating time is reduced by each measurement and some modeling of the complex system.

  Preferably, the following formula is used:

ここで無次元数Aおよびｗは、フィッティングにより定められたパラメータ値であり、
f_xは、

Here, dimensionless numbers A and w are parameter values determined by fitting,
f _x is

により定められ、ここで、a₁₀、a₁₁、a₁₂、p₁₁、p₁₂、q₁₁、およびq₁₂は、フィッティングによって求められる無次元パラメータ値であり、
無次元数x＝F（E_o ^x−EMF）／RT、
Fは、ファラデー定数（96485Cmol^-1）、
EMF（V）は、測定起電力値、
Rは、気体定数（8.314J（molK）^-1）、
Tは、（周囲）温度（K）、
｜x｜は、xの絶対値、
s_xは、xのサイン、
E_o ^xは、フィッティングによって得られるパラメータであり、
f_zは、

Where a ₁₀ , a ₁₁ , a ₁₂ , p ₁₁ , p ₁₂ , q ₁₁ , and q ₁₂ are dimensionless parameter values determined by fitting,
Dimensionless number x = F (E _o ^x −EMF) / RT
F is the Faraday constant (96485 Cmol ^-1 ),
EMF (V) is the measured electromotive force value,
R is a gas constant (8.314 J (molK) ⁻¹ ),
T is the (ambient) temperature (K),
| X | is the absolute value of x,
s _x is the sign of x,
E _o ^x is a parameter obtained by fitting,
f _z is

により定められ、ここで、a₂₀、a₂₁、a₂₂、p₂₁、p₂₂、q₂₁、およびq₂₂は、フィッティングによって求められる無次元パラメータ値であり、
無次元数z＝F（E_o ^z−EMF）／RT、
｜z｜は、zの絶対値、
s_zは、zのサインである。

Where a ₂₀ , a ₂₁ , a ₂₂ , p ₂₁ , p ₂₂ , q ₂₁ , and q ₂₂ are dimensionless parameter values determined by fitting,
Dimensionless number z = F (E _o ^z −EMF) / RT,
| Z | is the absolute value of z,
s _z is the sign of z.

  To include the effect of temperature in the SoC = f (EMF) relationship, the linear dependence of each model parameter is assumed,

ここで、T_refは参照温度（例えば25℃）であり、
Tは、周囲温度であり、
par（T_ref）は、温度T_refでの、EMF＝f（SoC）のモデルパラメータの一つの値である。Δpar値は、各パラメータpar（T_ref）において求められた、温度に対する感度である。

Where T _ref is the reference temperature (eg 25 ° C.)
T is the ambient temperature,
par (T _ref ) is one value of the model parameter of EMF = f (SoC) at the temperature T _ref . The Δpar value is a sensitivity to temperature obtained in each parameter par (T _ref ).

  The second new method described in this example is a method for determining the remaining operating time without the need for battery overvoltage prediction, battery voltage measurement, and the use of an EMF model under current-carrying conditions. In addition, a decrease in the accuracy of the remaining operation time is suppressed (see Table 1).

For this reason, a new predictive SoC ₁ function has been proposed as shown below.

ここで、SoC_st[％]は、Cレート電流Cおよび温度T[℃]での放電開始時のSoCを表し、
β[T^-1]、δ[T^-1]、ならびに無次元数α、γ、ζ、およびυは、測定SoC₁データにフィッティングされたパラメータである。

Here, SoC _st [%] represents the SoC at the start of discharge at C rate current C and temperature T [° C.]
β [T ⁻¹ ], δ [T ⁻¹ ], and dimensionless numbers α, γ, ζ, and υ are parameters fitted to the measured SoC ₁ data.

The SoC ₁ function shown in Equation 9 makes it possible to directly predict the remaining operating time at point B after discharge starts at point A (see Fig. 2). The function has a parameter set, which is obtained by fitting to available SoC ₁ measurements. The advantages are (i) ease of measurement of SoC ₁ (see Figure 2), (ii) no need for overvoltage prediction, voltage measurement and EMF model calculation under load conditions, and (iii) one function The remaining operating time is calculated directly. The first advantage improves the patented residual operating time indication algorithm. This is because more accurate SoC ₁ calculation is possible. The second advantage is that it eliminates the need for overvoltage prediction, voltage measurement, and EMF model calculations under load conditions. A third advantage is that the number of measurements and calculations for predicting the remaining operation time is suppressed as compared to the conventional remaining operation time prediction method.

The main problem in designing an accurate SoC instruction system is the process of battery degradation. For example, in a Li-ion battery, characteristics deteriorate due to an increase in impedance and / or a decrease in maximum capacity during the life of the battery. The rate of change of battery impedance and maximum capacity is highly dependent on operating conditions. At high C rates of charge / discharge current, and high and high voltage levels during battery charging, these two battery characteristics change rapidly. To illustrate these phenomena, FIG. 3 plots discharge battery capacity (Q _d ) as a function of cycle number for two different operating conditions. In both examples, the discharge battery capacity was predicted by coulomb calculations from a complete discharge step at 0.5C rate current.

  The decrease in discharge capacity is

で表される。ここでQ_dd[％]は、jサイクル後のQ_d[mAh]の低下を表す。

It is represented by Here, Q _dd [%] represents a decrease in Q _d [mAh] after j cycles.

FIG. 3 shows that the decrease in Q _d is highly dependent on operating conditions, ie, charge / discharge C-rate current, charge voltage limit and temperature. For example, during operating conditions for a battery of Q _dl (solid line in FIG. 3), the battery is charged to 4.3 V at 25 ° C. in a constant current constant voltage (CCCV) method. During the CC step, 4C rate current is applied. FIG. 3 shows that after 220 cycles, Q _dl is 675 mAh. On the other hand, after the first cycle, this is 1165 mAh. From this example, after 220 cycles, the Q _dl value is expected to drop to about 42% compared to the Q _dl value after the first cycle. In the second case (dashed line in FIG. 3), the battery is partially charged / discharged at approximately 0.5% rate current, 25 ° C., between approximately 30% and 70% SoC. From Figure 3, Q _d2, after 2000 cycles, whereas a value of 935mAh, Q _d2 after the first cycle is found to be 1150 mAh. Therefore, Q _d2 is reduced by 19% after 2000 cycles compared to Q _d2 after the first cycle.

It should be noted that the decrease in discharge capacity shown in FIG. 3 is a result of two combinations of battery processes, namely, an increase in battery impedance and a decrease in the maximum capacity of the battery. Due to the increase in battery impedance, capacity removal is less under similar discharge C-rate current from a degraded battery compared to a new battery. It can also be concluded that an increase in battery impedance leads to an increase in battery SoC ₁ . Due to the decrease in the maximum capacity of the battery, less capacity is stored in the battery (removed from the battery) during charging (discharging). The above example shows that battery degradation is a complex process involving many battery parameters such as impedance and capacity, and the most important characteristic seems to be the maximum capacity of the battery. However, changes in both parameters must be taken into account for more accurate determination of the SoC.

  Based on the above findings, Philips Research is an SoC instruction that combines the advantages of direct measurement and bookkeeping using a compatible and predictable system as described in US Pat. No. 6,420,851. Developed a method. The main feature of this method is that the SoC is predicted by voltage measurement when the battery is in a so-called equilibrium state and current measurement when the battery is in an unbalanced state. In equilibrium, no or little external current flows and the battery voltage is completely relaxed from the previous charge or discharge. As mentioned above, the measured battery voltage is substantially equal to the battery EMF at equilibrium conditions. Therefore, the EMF method can be applied under these conditions. When the battery is in an unbalanced state, the battery is either charged or discharged, and the charge drawn from or supplied to the battery is calculated by current integration. This charge is subtracted from or added to the previously calculated SoC value.

In addition to predicting the SoC, which is an indicator of the amount of charge still present inside the battery, this method can also predict the remaining operating time of the application under predetermined conditions. This is done by predicting the time until the battery voltage drops below the so-called discharge completion voltage (V _EoD ). This is the minimum voltage at which the application will no longer function. To predict this time, the overvoltage value for the selected load condition is predicted based on the current value of the SoC, the stored EMF curve and the so-called overvoltage function. When the battery is discharged, its voltage can be obtained by subtracting the overvoltage from the EMF value. Overvoltage depends on several factors including SoC, current, temperature and time, and also on factors such as degradation and battery chemistry. This SoC indication method is described in US Pat. No. 6,420,851, which later calibrates parameter values to deal with battery degradation as described in WO 2005/085889. And it is extended to be able to incorporate several methods for updating. Recently, new measurement methods have been obtained and published within the scope of the ph.D. project. Better execution of battery functions, namely EMF curves and overvoltage functions, mainly through new adaptive and predictive methods, and by reversing the function of SoC = f (EMF) and new methods to model SoC ₁ Improvements from have been made.

In order to cope with the effects of deterioration and improve the calculation accuracy of SoC, a new compatibility prediction method as described in International Publication No. WO2005 / 085889 has been developed. For example, the system described in this document adapts the maximum battery capacity and battery overvoltage model parameters, taking into account the effects of degradation. In this compatible method, the maximum capacity is updated without loading the battery with a full charge / discharge cycle. Assuming a start from equilibrium, the battery is charged or discharged for a maximum amount of charge, after which the battery returns to equilibrium and the maximum capacity is the SoC [% before and after the charge or discharge step. Is easily calculated by correlating it with the absolute amount of charge [C] during discharge from or to the battery during the applied charge / discharge step. In existing systems, full charge / discharge cycles are always applied and the maximum available battery capacity is required. Also, the above-mentioned compatible method uses the ratio of measured charge overvoltage (η _ch ^a / η _ch ^f ) between the degraded battery and the new battery, as well as the overvoltage symmetry phenomenon, and the overvoltage model parameter affects the degradation. Adapted to have. The voltage prediction method further has an extended EMF method and a maximum capacity method and is useful during the relaxation process. As a result, the calibration and compatibility of the SoC algorithm is improved.

Using the SoC algorithm described above, we conducted a series of tests to fully discharge a degraded battery at a constant C rate current at 25 ° C, and verified the accuracy of the SoC and remaining operating time. Using a conventional method, a battery with a maximum capacity of 1108 mAh and a value of η _ch ^a / η _ch ^f ratio of 1.4 was measured during the first charge cycle. Table 2 summarizes the experimental results (see Table 1).

[Table 2] Results obtained using the conventional SoC algorithm for degraded batteries

Table 2 suggests that at 25 ° C, 0.1C rate current, 98.2% of the SoC at the start of discharge, the remaining operating time is 577.2 minutes. However, the battery reached the level of V _EoD after 595.2 minutes. This means that the accuracy of the remaining operating time of the SoC system is -18.0 minutes. In this example, the relative error of the remaining operation time _trre was calculated to be -3.0% (see Equation 4). From Table 2, it was confirmed that the conventional SoC algorithm did not show sufficient accuracy for the remaining operation time when the battery deteriorated even when the battery parameters were updated.

Also, in Table 1, accurate modeling of the relationship of EMF = f (SoC) and overvoltage in order to obtain high accuracy for the remaining operating time is as follows when the battery is partially discharged even in a new battery: It was shown that it was difficult. This resulted in the development of new functions for SoC = f (EMF) and residual charge state (SoC ₁ ). By using these functions, the accuracy of the remaining operating time obtained for a new battery was significantly improved. However, as described above with respect to FIG. 3, the SoC ₁ value increases during the life of the battery. In order to be able to accurately calculate the remaining operating time during battery degradation, the changing behavior of SoC ₁ must be taken into account.

The EMF of Li-ion batteries can depend on degradation to some extent when plotted on the SoC [%] scale. In order to confirm the EMF dependence of degradation, the discharge EMF measured in a new battery (EMF _f ) was compared to the EMF obtained for the battery shown in FIG. 4 at 25 ° C. For accurate comparison, the maximum capacity of the battery was first grasped by using the method described in International Publication No. WO2005085889. As a result, capacity loss of 5.4% and 25.4% was observed for the battery shown in FIG. 3 (see Equation 10). The difference between EMF _f and EMF obtained with a 5.4% capacity loss battery (EMF _a5.4% ), and the value obtained with a 25.4% capacity loss battery, EMF _{a25.4%, to induce the eyes} The difference is plotted in FIG.

4 and 5 show that EMF changes with deterioration. The maximum difference between EMF _f and EMF _a5.4% was observed to be 32 mV at 2% SoC. This is because EMF is modeled only by EMF _f , and when using EMF without considering the effects of degradation, the SoC instruction system based on EMF is actually 2% SoC for degraded batteries when the SoC value is 2.4%. Means to show a value. The inaccuracy calculated by the difference between the true SoC value measured with a degraded battery and the SoC value measured with a new battery is -0.4%. From FIGS. 4 and 5, the difference between the EMF of the new battery and the EMF of the deteriorated battery increases with deterioration. For example, between EMF _f and EMF _a25.4% , a difference of -48mV is obtained with 57.4SoC. This is because, by using EMF obtained only by modeling EMF _f and without considering the effects of degradation, the SoC instruction system based on EMF, when the actual SoC value is 46.9% in a degraded battery, It means displaying SoC value of 57.4%. The inaccuracy will be -10.5%.

A solution to deal with SoC-EMF and SoC ₁ degradation dependencies is to store SoC-EMF and SoC ₁ values as a function of cycle number in the form of a look-up table. The lookup table is a table in which fixed values of measurement parameters are stored and used to display SoC-EMF and SoC ₁ changes during battery life. The size and accuracy of the lookup table in the SoC instruction system depends on the number of stored values. One of the main problems with this method is that even with a single battery type, it is difficult for the user to predict the SoC indications and to predict the battery behavior during battery life to provide accurate SoC indications That is. The lookup table method makes the process more complex and expensive compared to other methods when different battery types / chemical properties need to be handled, possibly not providing any significant advantage .

In summary, the main problem of the conventional SoC instruction method is that when the battery deteriorates, the SoC ₁ modeling accurately discharges the SoC ₁ and the accurate SoC calculation and accurate It is difficult to calculate the remaining operation time. With a look-up table, it seems most attractive to use a simple conformance system in an available way considering the degradation process. However, current methods using lookup tables known in the literature are problematic because it is difficult to predict the user's extended prediction and battery behavior for each battery type, leading to reduced prediction accuracy of SoC and remaining operating time.

In light of the foregoing, in a preferred embodiment of the present invention, a method for measuring the relationship between state of charge (SoC) and EMF is provided, which method comprises charging a battery from a low state of charge (SoC). Determining the maximum capacity of the battery, discharging the battery until the state of charge (SoC) drops to a predetermined rate, leaving the battery for a predetermined time, and EMF and state of charge (SoC) And obtaining the last three steps until V _EOD is _reached .

  Also, in a preferred embodiment, a device as described above is provided, and the device further provides a means for determining the maximum capacity of the battery by charging the battery from a low SoC and until the SoC decreases to a predetermined rate. , Means for discharging the battery, means for leaving the battery for a predetermined time to determine the EMF and SoC, and means for substituting the measured value into the memory.

  It has to be noted here that the above-mentioned model is mainly adapted to improve the relationship between EMF and SoC during battery degradation.

The basis of the proposed EMF adaptation method is a maximum capacity and constant current intermittent titration technique (GITT) measurement method combined with a voltage relaxation model. In the present application, the compatible EMF method may be applied to the following measurement method. First, for an accurate fit of the EMF model, the maximum capacity of the battery is determined during a complete charge cycle from a low SoC value, eg, less than 1% SoC. The battery is fully charged by the normal constant current constant voltage (CCCV) charging method, which is described in HJ Bergveld et al., “Battery Management System-Designed by Modeling”, Philips Research Book Series, vol. It is described in Kluwer Academic Publishers, 2002, Chapter 6. The maximum capacity is calculated by the method described in International Publication No. WO2005085889. The battery is further discharged to a 4% SoC step with a 0.1 C rate current. A 12 hour rest time follows the discharge step. At the end of the rest period, the battery reaches equilibrium. As a result, the first EMF point, EMF ₁ , having the corresponding SoC is obtained (see FIG. 6). The discharge is repeated at different temperatures until the battery voltage reaches the V _EoD level. An example measurement for seven EMF points using a 4% SoC discharge step at 25 ° C. is shown in FIG.

  Although the selected C rate current, SoC step and rest period values facilitate the implementation of the EMF compliance method, the method described above is not limited to any particular C rate current, discharge SoC step, or rest period, and therefore It is possible to operate under various conditions. For example, an alternative method to avoid long rest periods uses a conventional voltage relaxation model. From the analysis of the voltage relaxation model, it has been observed that a 15-minute rest period always gives better accuracy than 0.5% SoC within the extended conditions. For this reason, a 15 minute rest period is considered sufficient for accurate application of battery EMF. However, this does not eliminate any other relaxation time.

Consider further the example of applying EMF to a 5.4% capacity loss battery at 25 ° C. For example, in this example, consider 10 EMF prediction points distributed along the horizontal axis during discharge. During the first 15 minutes of the rest period, the measured voltage and time samples are treated as input to the voltage relaxation model. In this example, we consider SoC levels of 0 and 100% at the corresponding EMF values. Furthermore, 12 EMF points are fitted using a method that takes into account the curve shape. The resulting EMF is shown in FIG. Comparison with EMF (GITT method) obtained by long-term relaxation time was examined. 8, in order to show the results of the proximity of the voltage prediction (V _p) method, were plotted the difference between the EMF obtained by EMF and V _p method obtained in GITT method.

  From FIGS. 7 and 8, in the 1.1% SoC, the maximum EMF difference is 36 mV. This is because the actual SoC value calculated based on the discharge EMF is 1.1%, while using the EMF adaptation method, in this case, the SoC instruction system based on the EMF produces a SoC value of 1.3% It means to show. The inaccuracy is 0.2% SoC. This effect becomes more prominent in the flat region of the EMF-SoC curve, and a large error occurs in the SoC even if the difference in EMF is smaller. For example, a difference of about 8 mV gives 67% SoC. In this case, the EMF compliance method leads to 1% SoC inaccuracy. From the previous situation, which provided a newly developed EMF calibration method from Figures 7 and 8, only 10 predicted EMF points were used after 15 minutes of relaxation to obtain a new EMF curve for the degraded battery. Sometimes, it can be seen that the SoC accuracy improvement of 1% or more is always obtained. EMF conformance accuracy is easily improved by considering longer relaxation times for the voltage relaxation model or by considering more EMF points due to the fitting method.

The second new method of the present application is the SoC ₁ adaptation method, in which the parameters of the SoC ₁ model are adapted in consideration of the battery degradation process. At each time after the battery is discharged to the V _EoD level, the EMF value can be predicted in the first few minutes of the relaxation process by a conventional voltage relaxation model. FIG. 9 shows a measurement example. This figure shows _{what happens} to the battery open circuit voltage (OCV) after applying a discharge step from a 100% SoC at a _0.1C rate at 25 ° C to the V _EoD level. . The predicted voltage V _p was compared based on the measured OCV, OCV _m during the first 15 minutes of the relaxation process. Measurements were performed with a 5.4% capacity loss battery.

  Accordingly, in a preferred embodiment, a method of the type described above is provided, and after the completion of the discharge process, by determining the battery's EMF value by extrapolation of the battery voltage taken during relaxation after the charge or discharge process, EMF values are predicted. This extrapolation uses only the variables taken during the mitigation process and uses the predetermined relationship between the battery EMF and the state of charge (SoC) to derive the battery state of charge (SoC) from the battery EMF. Based on an extrapolation model.

As can be seen from FIG. 9, during the relaxation process, the battery OCV does not match the EMF after the discharge step. The value of the battery OCV changes from 3.0V to about 3.37V after 720 minutes after current interruption. From FIG. 9, the predicted voltage value based on OCV measurements in the first 15 minutes of the relaxation process is very close to the EMF value measured after 720 minutes. In this example, a difference of 13 mV is measured. The predicted EMF value is further obtained as an input to the previously described fitted SoC = f (EMF) model. As a result, the SoC [%] value representing the new SoC ₁ value is calculated under the applicable measurement discharge conditions. In this example, the SoC value by EMF, by comparison with EMF by V _p, -0.1% of SoC inaccuracy is calculated. From the situation described above in FIG. 9 and each time after discharging the battery until it reaches the V _EoD level, it can be said that the new SoC ₁ value is accurately determined by the relationship between V _p and SoC = f (EMF).

  Hereinafter, the present invention will be described with reference to the drawings.

It is a graph which shows the precision of SoC instruction | indication by the EMF = f (SoC) model in the conventional condition. leading to an empty battery at t _r = t _empty, schematically shows a curve of the EMF (dashed line) and discharge voltage (solid line). It is a graph which shows the fall of the discharge capacity of the rechargeable battery in deterioration. Fig. 6 is a graph showing EMF as a function of battery degradation. 6 is a graph showing EMF differences as a function of battery degradation. 6 is a graph showing EMF during a measurement process according to a preferred embodiment. It is a graph of both calculated EMF and measured EMF. It is a graph which shows the difference between calculation EMF and measurement EMF. It is a graph which shows the estimated voltage and open circuit voltage after a discharge step. 1 is a schematic view of a battery having features of the present invention. It is a graph which shows the result of the present invention. It is a graph which shows the precision obtained by this invention. It is a graph which shows the difference between the measurement result obtained by this invention, and the fitting result. FIG. 2 illustrates a system for updating parameters according to a preferred embodiment.

Newly proposed SoC = f (EMF) and SoC ₁ models as described above can be used significantly in previous SoC ₁ instruction algorithms. However, it can be used as well for any SoC system that uses battery EMF to determine the SoC or indicate the remaining run time.

FIG. 10 shows a general block diagram for executing SoC = f (EMF) and SoC ₁ method in the SoC instruction system. The battery voltage V _bat , current I _bat , and temperature T _bat are measured from an analog preprocessing unit, which includes, for example, filtering, amplification, and digitization. The digital representation of the battery variable is supplied to digital processing means such as a microcontroller. The SoC = f (EMF) and SoC ₁ methods are run on this digital processing unit, like any SoC instruction system based on the EMF method. The unit also uses memory, which may be external memory or memory residing on the same silicon die. Using ROM memory, battery specific data such as EMF or SoC ₁ model may be stored in advance as a function of temperature if possible. For example, measured EMF and T samples are temporarily stored in RAM memory, and EMF curves are stored in ROM in the form shown in Equation 5-8. Next, the digital processing means acquires these measurement results, and models and calculates the SoC. Similarly, the digital processing unit calculates the remaining operating time based on the current, SoC start, temperature measurement results, and stored SoC ₁ model. The predicted SoC and remaining operating time may be displayed directly to the user via a display or communicated with others via a digital interface. For example, the latter situation occurs when the digital processing means shown in FIG. 10 is in a dedicated SoC and a remaining operating time indication IC, which sends the SoC and remaining operating time data to the mobile device host. Transfer to processor.

  Equations 5-8 are used to fit the SoC = f (EMF) relationship to the measured charge / discharge EMF curve obtained in the reference battery tester at three temperatures. The charge / discharge EMF curve may be measured by a conventional voltage relaxation method. From FIG. 11, it can be seen that the modeled discharge EMF curve using the system shows a good fit to the measurement curve obtained in the reference battery tester at all temperatures.

From FIG. 11, it can be said that the maximum error in the SoC of 0.8% SoC is about 85% SoC at 5 ° C. For this reason, it can be concluded that the newly developed SoC = f (EMF) function shows high accuracy in the SoC calculation in equilibrium (see also Figure 1). To get information about SoC ₁ , the batteries are discharged from different SoC _sts at different constant C rates and temperatures. The SoC value at the completion of discharge is regarded as the SoC ₁ value. Another possibility to determine the SoC ₁ value is to apply the voltage relaxation model and the SoC = f (EMF) relationship shown in this application. In this way, after the first few minutes of the voltage relaxation curve, the predicted battery equilibrium voltage is converted to a SoC ₁ value using the SoC = f (EMF) function shown here. After verification, we observed that a similar prediction of the SoC ₁ value was obtained by the method described above. As a result, the measured SoC ₁ value is considered as an input for the SoC ₁ model represented by Equation 9. FIG. 12 shows the measurement result (SoC _1m ) and the fitting (SoC _1f ) SoC ₁ value result.

In FIG. 13, the difference between the measured SoC ₁ value and the fitting SoC ₁ value is plotted to further illustrate the accessibility between the measured data and the fitting data. 12 and 13, it was found that the maximum difference between the measured data and the fitting SoC ₁ was 0.6% at 45 ° C.

  To prove the accuracy of the SoC and the remaining operating time, a test similar to the above (see Table 1) was performed using the improved SoC algorithm. Table 3 shows the results obtained.

[Table 3] Results from the improved SoC algorithm obtained in the extended condition range

In the example in Table 3, at 25 ° C, 0.5C rate current, at the start of 36.2% SoC discharge, the system showed a residual run time of 42.6 minutes. The remaining operating time was calculated from Equation 3, using the new SoC = f (EMF) and SoC ₁ methods. After 42.3 minutes, the battery reached a level of 3V and an accuracy of 0.3 minutes was calculated for the remaining run time. On the other hand, the relative error of the remaining operation time was 0.7%. Table 3 shows that the newly developed SoC = f (EMF) and SoC ₁ methods significantly improve the prediction accuracy of the remaining operation time.

In summary, the proposed method of calculating the SoC and predicting the remaining operating time uses the SoC = f (EMF) model of Equation 5-8 during equilibration, and the Coulomb calculation of Equation 9 during discharge. Combine SoC ₁ models. The results presented in this application (see Table 3) show that SoC and remaining operating time can be predicted with an accuracy of less than 1%. The advantages of the method and apparatus according to the invention are as follows:
-Accurate evaluation of SoC based on EMF while the battery is in equilibrium,
-During equilibration, no mathematical inversion is required when determining the SoC, such as the traditional EMF = f (SoC) model,
-The system of the present application can accurately determine the remaining operation time based on the SoC ₁ method under any load conditions in addition to the SoC calculation (see Table 3).
-Battery overvoltage calculation under load conditions, voltage measurement, and EMF model calculation, which are necessary in the conventional prediction method of remaining operating time, are unnecessary.
-The new SoC = f (EMF) and SoC ₁ methods presented here are simple and can be adapted to account for battery degradation.

As mentioned above, the newly proposed SoC-EMF and SoC ₁ compatible system can be used significantly in conventional SoC instruction algorithms. However, it can be used for any SoC system that uses battery EMF to define the SoC and indicate the remaining run time. FIG. 14 shows a general block diagram for executing the SoC-EMF and SoC ₁ adaptation method in the SoC instruction system.

The SoC value is calculated by measuring the battery voltage (V _bat ) and temperature (T _bat ) and the stored SoC-EMF model (SoC-EMF _m ) when the battery is in equilibrium. During current-carrying conditions, the remaining operating time value is calculated by the battery current (I _bat ) and temperature measurements, and the SoC ₁ model SoC _1m . SoC-EMF _m and SoC _1m have a set of parameters, par ₁ , ..., par _n , which are updated as the battery degrades, allowing more accurate battery SoC and remaining operating time calculations become. After each current interruption, a new set of battery variables V _bat and T _bat are measured and the SoC calibration and prediction algorithm predicts new EMF (SoC-EMF _m ^es ) and SoC ₁ (SoC _{1 m} ^es ) values . These predicted values are stored in a memory such as an EEPROM. This process is repeated an arbitrary number of times after the current interruption. The prediction sample is further fed to a calibration unit, which determines the update of the SoC-EMF _m and SoC _1m parameter sets par ₁ ,..., Par _n that are used to calculate the SoC and remaining operating time. (See Figure 14). Any optimization algorithm may be used as the adaptation algorithm, examples of which are shown in the published literature. It should be noted that this configuration may be performed with any value of V _bat and T _bat , _{depending on} the implementation of the adaptation system described herein.

To confirm the accuracy of the SoC and remaining operating time, a new set of tests including partial battery discharge was performed using a compatible SoC algorithm at 25 ° C and different constant C rate currents. During these tests, a 5.4% capacity loss battery was selected. In addition, in order to verify that high accuracy can be obtained in the remaining operation time based on the SoC = f (EMF) relation and modeling accuracy and suitability for SoC ₁ in the extended condition range, a partial discharge battery was examined. This is significant when compared to conventional algorithms where even a new battery results in inaccurate residual operating time under partial discharge conditions. Table 4 shows the results obtained (see comparison with Table 1).

[Table 4] Result of adaptive SoC algorithm obtained for degraded batteries

From Table 4, the system showed a residual operating time of 110.8 minutes at the start of a discharge performed from a 20.1% SoC with a 0.10C rate current at 25 ° C. After obtaining new parameter values for the SoC-EMF and SoC ₁ models using the calibration system shown in this application, the remaining operating time was calculated by Equation 3. After 108.8 minutes, the battery reached a level of 3V, the accuracy of the remaining operating time was 2.0 minutes, and the relative error was calculated as 1.8%. Table 4 shows that the newly developed compatible system improves the predictability of the remaining operating time of the deteriorated battery.

The present invention can be applied to portable battery power supply devices, and is not particularly limited to Li-ion batteries. The present invention can be used in combination with an SoC indication algorithm, at least in part based on the EMF method, and allows accurate prediction of a battery SoC even during battery degradation. The earlier Philips Research patents do not include the idea of adapting EMF and SoC ₁ methods to account for battery degradation processes. Various examples of portable devices powered by a rechargeable lithium ion battery can be recognized both inside and outside the Philips organization.

Claims (22)

A method for determining a state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery,
Defining a function including a parameter between the state of charge (SoC) and the electromotive force (EMF) of the rechargeable battery;
Measuring a plurality of values of the state of charge (SoC) of the rechargeable battery as a function of the electromotive force (EMF);
Fitting the parameter of the function to the result of the measurement;
Storing the function including fitting parameters in a memory;
Obtaining the electromotive force; and
Putting the measured value of the electromotive force into the function;
Reading the state of charge (SoC);
Having a method. The function is

Where the dimensionless numbers A and w are parameter values determined by fitting,
f _x is

Where a ₁₀ , a ₁₁ , a ₁₂ , p ₁₁ , p ₁₂ , q ₁₁ , and q ₁₂ are dimensionless parameter values determined by fitting,
Dimensionless number x = F (E _o ^x −EMF) / RT,
F is the Faraday constant (96485 Cmol ^-1 ),
EMF (V) is the measured electromotive force value,
R is a gas constant (8.314 J (molK) ⁻¹ ),
T is the (ambient) temperature (K),
| X | is the absolute value of x,
s _x is the sign of x,
E _o ^x is a parameter obtained by fitting,
f _z is

Where a ₂₀ , a ₂₁ , a ₂₂ , p ₂₁ , p ₂₂ , q ₂₁ , and q ₂₂ are dimensionless parameter values determined by fitting,
Dimensionless number z = F (E _o ^z −EMF) / RT
| Z | is the absolute value of z,
2. The method of claim 1, wherein s _z is a sign of z. The measurement is repeated at least once at a temperature different from the temperature during the previous measurement;
The measurement result is stored together with the plurality of temperatures at which the measurement was performed,
The following function parameter fitting is performed,

par (T) = par (T _ref ) + (T−T _ref ) Δpar

Where T _ref is the reference temperature (eg 25 ° C.)
T is the ambient temperature,
par (T _ref ) is one value of the SoC = f (EMF) model parameter embedded in the function of claim 2 at temperature T _ref ;
3. The method according to claim 2, wherein Δpar is a sensitivity to temperature obtained for each parameter par (T _ref ) with respect to the measurement result. A method for determining a remaining operating time of a rechargeable battery by performing the method of claim 1, 2, or 3 to determine the state of charge (SoC),
The remaining time is determined from the state of charge (SoC).

Is calculated using
SoC _st [%] represents the SoC at the start of discharge at C rate current C and temperature T [° C]
β [T ⁻¹ ], δ [T ⁻¹ ], and dimensionless numbers α, γ, ζ, and υ are parameters fitted to the measured SoC ₁ data. A method for measuring a relationship between the state of charge (SoC) and the EMF, wherein the method is used in the method according to any one of claims 1 to 4.
Determining the maximum capacity of the battery by charging the battery from a low state of charge (SoC);
Discharging the battery until the state of charge (SoC) drops to a predetermined rate;
Leaving the battery for a predetermined time;
Repeating the last three steps until V _EOD is reached;
Having a method.   6. The method according to claim 5, wherein the charging to the maximum capacity is performed by a constant current constant voltage method.   The method according to claim 5 or 6, wherein the predetermined percentage is between 1% and 10%.   8. The method according to claim 5, 6 or 7, characterized in that the predetermined time is between 5 minutes and 1 hour, preferably 15 minutes.   9. A method according to claim 5, 6, 7, or 8, characterized in that the method is repeated at least once at a temperature different from the temperature at which the first method was performed. The EMF is determined by extrapolation of the battery voltage taken during relaxation after the discharge process,
10. The method according to any one of claims 5 to 9, wherein the extrapolation is performed based on an extrapolation model using only variables collected during the relaxation process. 11. A method according to any one of the preceding claims, wherein after discharge to V _EOD level, SoC ₁ is determined using the determined relationship between EMF and SoC. After completion of the discharge process, the EMF value is predicted by determining the EMF of the battery by extrapolating the battery voltage taken during the relaxation process after the discharge process,
The extrapolation is based on an extrapolation model using only variables collected in the relaxation process,
12. The state of charge (SoC) of the battery is obtained from the EMF of the battery by using a predetermined relationship between the EMF and state of charge (SoC) of the battery. the method of. A device for determining a state of charge (SoC) of a rechargeable battery as a function of the electromotive force (EMF) of the battery,
Means for determining the state of charge and the EMF in the battery;
A memory adapted to store a parameterized relationship between the state of charge (SoC) and the electromotive force (EMF) of the rechargeable battery;
Means for adapting the parameters of said relationship;
Having equipment. The function is

Where the dimensionless numbers A and w are parameter values determined by fitting,
f _x is

Where a ₁₀ , a ₁₁ , a ₁₂ , p ₁₁ , p ₁₂ , q ₁₁ , and q ₁₂ are dimensionless parameter values determined by fitting,
Dimensionless number x = F (E _o ^x −EMF) / RT,
F is the Faraday constant (96485 Cmol ^-1 ),
EMF (V) is the measured electromotive force value,
R is a gas constant (8.314 J (molK) ⁻¹ ),
T is the (ambient) temperature (K),
| X | is the absolute value of x,
s _x is the sign of x,
E _o ^x is a parameter obtained by fitting,
f _z is

Where a ₂₀ , a ₂₁ , a ₂₂ , p ₂₁ , p ₂₂ , q ₂₁ , and q ₂₂ are dimensionless parameter values determined by fitting,
Dimensionless number z = F (E _o ^z −EMF) / RT,
| Z | is the absolute value of z,
14. The device according to claim 13, wherein s _z is a sign of z.   The device has means for measuring the temperature of the battery and storing the relationship between state of charge (SoC) and electromotive force (EMF) as a function of the temperature, and the relationship at the temperature is determined. 15. The device according to claim 13 or 14, characterized in that: A device for determining the remaining operating time of a rechargeable battery,
Having means for performing the following relationship calculations:

Here, SoC _st [%] represents the SoC at the start of discharge at C rate current C and temperature T [° C.]
β [T ^-1 ], δ [T ^-1 ], and dimensionless numbers α, γ, ζ, and υ are parameters fitted to the measured SoC ₁ data. A device according to any one of the preceding claims,
further,
Means for determining the maximum capacity of the battery by charging the battery from a low SoC;
Means for discharging the battery until the SoC drops to a predetermined rate;
Leave the battery for a predetermined time,
Means for determining the EMF and the SoC;
Means for substituting the measured value into the memory;
Having equipment. The instrument is adapted to predict the EMF value by determining the EMF of the battery by extrapolating the battery voltage taken during the relaxation period after the discharging process;
The extrapolation is based on an extrapolation model using only variables taken during the relaxation process,
The device according to claim 17, wherein the obtained EMF value is stored in a memory together with the SoC algorithm value obtained from Coulomb calculation.   19. A battery charger having a device for determining a state of charge (SoC) of a rechargeable battery according to any one of claims 13 to 18.   19. An electrical device adapted to be powered by a rechargeable battery comprising the device according to any one of claims 13-18.   A portable electronic device, such as a mobile phone, a GPS device or a shaver, comprising the device according to any one of claims 13 to 18. An electrically driven vehicle, such as a hybrid vehicle, comprising the device according to any one of claims 13 to 18 and a tow battery,
An electrically driven vehicle, wherein the device is adapted to determine a state of charge of the tow battery.

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